Byeongsu Sim

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance. Unfortunately, diffusion models have a critical downside - they are inherently slow to sample from, needing few thousand steps of iteration to generate images from pure Gaussian noise. In this work, we show that starting from Gaussian noise is unnecessary. Instead, starting from a single forward diffusion with better initialization significantly reduces the number of sampling steps in the reverse conditional diffusion. This phenomenon is formally explained by the contraction theory of the stochastic difference equations like our conditional diffusion strategy - the alternating applications of reverse diffusion followed by a non-expansive data consistency step. The new sampling strategy, dubbed Come-Closer-Diffuse-Faster (CCDF), also reveals a new insight on how the existing feed-forward neural network approaches for inverse problems can be synergistically combined with the diffusion models. Experimental results with super-resolution, image inpainting, and compressed sensing MRI demonstrate that our method can achieve state-of-the-art reconstruction performance at significantly reduced sampling steps.

Recently, deep learning approaches for accelerated MRI have been extensively studied thanks to their high performance reconstruction in spite of significantly reduced runtime complexity. These neural networks are usually trained in a supervised manner, so matched pairs of subsampled and fully sampled k-space data are required. Unfortunately, it is often difficult to acquire matched fully sampled k-space data, since the acquisition of fully sampled k-space data requires long scan time and often leads to the change of the acquisition protocol. Therefore, unpaired deep learning without matched label data has become a very important research topic. In this paper, we propose an unpaired deep learning approach using a optimal transport driven cycle-consistent generative adversarial network (OT-cycleGAN) that employs a single pair of generator and discriminator. The proposed OT-cycleGAN architecture is rigorously derived from a dual formulation of the optimal transport formulation using a specially designed penalized least squares cost. The experimental results show that our method can reconstruct high resolution MR images from accelerated k-space data from both single and multiple coil acquisition, without requiring matched reference data.